4p + 2q = 8 and q = 2p +1 solve by substitution
you have q = 2p+1
so, substitute into the other equation:
4p + 2(2p+1) = 8
4p + 4p + 2 = 8
8p = 6
p = 3/4
now you can get q.
be sure to check your answers in both equations, lest
a) you made a mistake
b) I made a mistake
Simplify: q – (7q + 1)
To solve the system of equations using substitution, we need to substitute the value of q from the second equation into the first equation.
Given:
1) 4p + 2q = 8
2) q = 2p + 1
Step 1: Substitute the value of q from equation 2 into equation 1:
4p + 2(2p + 1) = 8
Simplify the equation:
4p + 4p + 2 = 8
Combine like terms:
8p + 2 = 8
Step 2: Solve for p:
Subtract 2 from both sides:
8p = 8 - 2
8p = 6
Divide both sides by 8:
p = 6 / 8
p = 3/4 or 0.75
Step 3: Substitute the value of p into equation 2 to find q:
q = 2(0.75) + 1
Simplify the equation:
q = 1.5 + 1
Combine like terms:
q = 2.5
So, the solution to the system of equations is p = 3/4 or 0.75, and q = 2.5.
4p + 2q = 8
q = 2p +1
Rearrange either so it aligns, I'll rearrange the bottom.
4p +2q = 8
-2p - q = 8 (subtract 2p from both sides)
Pick one that simplifies easily I'll use the 4p one.
4p + 2q = 8
2q = 8 - 4p
q = 4 -2p
Substitute q value for q in opposite equation
-2p + (4 - 2p) = 1
-2p + 4 - 2p = 1
-4p = -3
p = 3/4
plug p in to find q